Best Known (53, 53+42, s)-Nets in Base 2
(53, 53+42, 36)-Net over F2 — Constructive and digital
Digital (53, 95, 36)-net over F2, using
- t-expansion [i] based on digital (51, 95, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
(53, 53+42, 41)-Net over F2 — Digital
Digital (53, 95, 41)-net over F2, using
(53, 53+42, 170)-Net in Base 2 — Upper bound on s
There is no (53, 95, 171)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 40970 263353 149525 423971 919872 > 295 [i]